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Description

The classical Minkowski problem is a central problem in convex geometry which asks that given a nonzero finite Borel measure $\mu$, what are the necessary and sufficient conditions on $\mu$ such that $\mu$ equals to the surface area measure of a convex body $K$. In this talk, I will present the general dual extension of the classical Minkowski problem---the generalized dual Orlicz-Minkowski problem. That is, for which nonzero finite Borel measures $\mu$ on $\sphere$ and continuous functions $\wp$ and $\psi$ do there exist $\tau\in \R$ and $K\in \cK_{o}^n$ such that $\mu=\tau\,\deV(K,\cdot)$ Here $\deV(K,\cdot)$ is the finite Signed Borel measure. In particular, a solution where $G$ and $\psi$ are increasing to this problem will be presented. This work is based on a joint work with Professors Richard Gardner, Daniel Hug and Deping Ye.